nLab hidden sector

Idea

In (perturbative) quantum field theory a hidden sector is a subspace of the space of fields whose only interaction with the remaining fields is via gravity.

If one interprets the remaining fields as constituting a model for phenomenology, then in the world this describes the fields in the subspace are literally hidden, they can only bee “seen” via their gravitational pull (or via gravitational waves).

Hidden sectors as a model for the real world remain hypothetical. They have been postulated notably as a means to explain supersymmetry breaking (see below). They appear generically in perturbative string theory vacua (further below) after KK-compactification.

Definition

Specifically in Lagrangian field theory this means that the field bundle $E \overset{fb}{\to} \Sigma$ over spacetime $\Sigma$ is a fiber product

$$E \underoverset{\simeq}{(p_1,P_2)}{\longrightarrow} E_{1} \times_\Sigma E_2$$

such that the interaction Lagrangian density $\mathbf{L}_{int}$ is of the form

$$\mathbf{L}_{int} = p_1^\ast \mathbf{L}_{int,1} + p_2^\ast \mathbf{L}_{int,2} + \mathbf{L}_{grav}$$

where the first two summands are pullbacks of interactions of the fields in $E_1$ and $E_2$ separately, while the last summand is the interaction term of gravity coupled to the respective fields jointly.

In this case $E_2$ is a sector hidden from $E_1$, and conversely.

Examples

In supersymmetry breaking

The concept of gravity-mediated supersymmetry breaking resulted from study of gaugino condensation in a hidden sector. (Nilles 01)

In string theory

In string theory hidden sectors appear naturally in various ways.

Hořava-Witten theory at finite interval length gives rise to a copy of heterotic supergravity at each of the “endpoints”, which, as gauge theories, interact with each others only via bulk gravity.

In models of M-theory on G₂-manifolds such as the G₂-MSSM, the 4d gauge-field content arises under KK-compactification from 3-cycles in the G₂-manifold fiber, and if two such do not intersect, they give rise to hidden sectors in the 4d physics. (e.g. Kane 17, section 4.4)

Related concepts

• soft supersymmetry breaking term

References

Discussion in the context of supersymmetry breaking is in

• Hans-Peter Nilles, Hidden Sector Supergravity Breakdown, Nucl. Phys. Proc. Suppl. 101 (2001) 237-250 (arXiv:hep-ph/0106063)

• Luis Ibáñez, Angel Uranga, section 2.6.5 of String Theory and Particle Physics – An Introduction to String Phenomenology, Cambridge University Press 2012

Discussion specifically in the context of the G₂-MSSM is in

• Gordon Kane, section 4.4 of String theory and the real world, Morgan & Claypool, 2017 (doi:0.1088/978-1-6817-4489-6)